Photographic blending of close binaries.
Douglas Duke · The Astronomical Journal · 1954
In order to find the individual masses of a visual binary system it is necessary to obtain the mass ratio. This is obtained by observing the fraction of the total relative orbital motion due to the brighter component. However, if the separation is less than 2" the stars will normally be blended on the photographic plate, and it is then necessary to correct the position of the blended center to obtain the position of the brighter star. It has previously been assumed that the position of the blended image will be the mean position of the components weighted for relative brilliance. This gives a blending correction p, which is a function only of the magnitude difference Am between components: = I + 1&AAm It is felt that the above assumption is not valid for two reasons: I. The response of the photographic plate is not proportional to the exposure received. 2. From personal experience it is believed that the plate measurer makes settings midway between the visible extremities of the image rather than on some interior point of maximum density. Blending corrections based upon the second of the above objections are not only functions of the magnitude difference, but depend also upon the actual separation between the components, the exposure level of the plate, and probably also on seeing conditions. These other variables enter because, in this assumption, the blending correction is: I I p = - - -AD 2 4d where d is the separation and AD is the difference in image diameter between components. Since, on the photographic plate, image diameter is not proportional to magnitude, AD will depend upon the exposure level. Any change of shape of the magnitude-diameter relation due to seeing differences or other causes will also be important. Since it is of interest to compare the results of the two methods an empirical magnitude- diameter relation was chosen at random and the blending corrections computed for different values of separation, exposure level and magnitude difference. Allowance was made for additional outward spread of the images due to the proximity of the components. Significant differences are found. In many cases the difference in the computed values of p for a given Am vary as much as 0.10 with different separations and exposures. In a few cases the difference approaches 0.20. If this is actually the case, errors of the order of twenty per cent may be introduced in the individual masses by use of the currently used formula for p. The only experimental work available as a check is that of R. G. Hall;' but his work affords only an incomplete comparison since he did not use different exposure levels or obtain results for greatly elongated images. Nevertheless the method here presented calls precisely for the discrepancy he found between observed and computed values of p. If the separation of the components is relatively small and the exposure average, the calculated values of p fall to zero, as Am increases, more rapidly than called for by the corrections now in use. Further observational tests are very desirable, and it is planned to observe a number of selected binaries under widely different seeing conditions and with varying exposures on the photographic plate. Should the predicted variations in blending be found, further experimental work with artificial stars will be undertaken.